Speed of Sound of Oxygen in Supercritical States up to 500 K and 100

Article pubs.acs.org/jced

Speed of Sound of Oxygen in Supercritical States up to 500 K and 100 MPa Frithjof H. Dubberke, Markus Riepold, Elmar Baumhögger, and Jadran Vrabec* Thermodynamics and Energy Technology, University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany ABSTRACT: Oxygen is the second-most abundant element in the earth’s atmosphere and plays an important role in various engineering applications. The precise knowledge of its thermophysical properties is thus important. As a fully fledged thermodynamic property, the speed of sound substantially contributes to the development and parametrization of equations of state. This work presents experimental speed of sound data for oxygen measured with an apparatus that is based on the pulse-echo technique with a double path-length. When working with pure oxygen at high temperatures and pressures, tight safety requirements have to be met, limiting the present measurements to 500 K and 100 MPa.

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INTRODUCTION For optimizing industrial processes and for scientific applications the precise knowledge of thermodynamic properties is crucial. Oxygen, which is behind nitrogen the secondmost abundant element in the earth’s atmosphere, plays a major role in many industrial applications. The most accurate equation of state (EOS) for oxygen was established in the year 1985 by Schmidt and Wagner.1 Highly accurate thermodynamic property data from experimental measurements are the basis for developing fundamental EOS2 and speed of sound data are well suited for this purpose. However, there is a lack of speed of sound data in the supercritical region at elevated temperatures and moderate pressures, as illustrated in Figure 1. Experiments with oxygen have been carried out by numerous authors and date back to the early 1900s, when Cook3 used Kundt’s tube20 for speed of sound measurements of oxygen and air. First ultrasonic measurements were accomplished in the 1930s, primarily in low pressure regions. Van Itterbeek and coworkers4,6−8,11,14,15 established an acoustic interferometer, enabling for measurements with uncertainties of about 0.1%. In 1938, Liepmann9 determined data for liquid oxygen using a light diffraction method for measurements at low temperatures. In the middle of that century, Galt,10 Boyer,12 and Verhaegen13 contributed further data for low temperature and pressure regions. In 1962, van Itterbeek and van Dael14 used the pulseecho method in the liquid region between 64 and 91 K and pressures of up to 92 MPa. Baidakov and Kaverin18 determined data with an uncertainty of 0.17% for superheated liquid oxygen for the first time in 1989, employing the pulse-echo technique by using an acoustic cell made out of glass. In 1999, Abramson at al.19 reached extremely high pressures of up to 12.6 GPa with a diamond-anvil cell, attaining an overall uncertainty of 2% in their measurements. An extensive study on the speed of sound © XXXX American Chemical Society

Figure 1. Experimental speed of sound data for oxygen: ●, Cook;3 #, Keesom et al.;4 ▼, Bär;5 bold +, van Itterbeek and Mariëns;6 ×, van Itterbeek and Mariëns;7 □, van Itterbeek and van Paemel;8 ■, Liepmann;9 ◇, Galt;10 ▲, van Itterbeek and de Bock;11 ⊕, Boyer;12 ⊞, Verhaegen;13 y, van Itterbeek and van Dael;14 ◆, van Dael et al.;15 ○, Blagoi et al.;16 ▽, Straty and Younglove;17 △, Baidakov and Kaverin;18 ◇ with cross, Abramson et al.;19 ☆, this work.

of compressed liquid oxygen was presented by Straty and Younglove17 in 1973, employing the pulse-echo technique. An overview of these data is given in Figure 1. The present work follows up on these measurements in a poorly sampled region, i.e. for temperatures between 300 and 500 K and pressures between 40 and 100 MPa. This region intentionally overlaps for Received: November 25, 2015 Accepted: February 28, 2016

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DOI: 10.1021/acs.jced.5b01007 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

velocities in pipes or components.29,30 According to the recommendation BGR 500,26 which demands an appropriate steel alloy with an accumulated mass fraction of chrome and nickel above 22%, the measurement cell was made out of highly corrosion resistant stainless steel (1.4571) and the cylindrical pressure vessel (sealed with a copper gasket) out of highly tensile steel (1.4462) that are both suitable for applications with pure oxygen.29,31−34 Pure copper has an ignition temperature of 1338 K in pure oxygen at 70 MPa.35 It is even harder to ignite than stainless steel36 and is recommended in the literature as ”particularly useful for resisting ignition by particle impact and therefore can be used in high-velocity gas applications for which burnresistant alloys are required”.28 The piezoelectric quartz crystal was connected by circular gold electrodes that do not hold any risks. The Teflon coated cables were mechanically connected to the gold electrodes and on the other end soldered, without using any flux, to the electrical feed through.24 Upon combustion even small amounts of material may liberate large quantities of energy, resulting into an increasing temperature. This may lead to a chain reaction if the ignition temperature of other materials is attained. Thus, the lowest ignition temperature of all materials in the apparatus must not be exceeded.29 Before use, the apparatus was very carefully cleaned and freed from impurities, especially of oily and greasy contaminants, which can induce a high risk due to their low ignition temperature.26,28 Before assembling all internal surfaces of the piping system including valves, both pressure sensors and the pressure cylinder were cleaned with acetone. After assembling, the system was evacuated and then flushed about five times with argon, at a temperature of 400 K. After a final evacuation, the system was flushed with oxygen for about 1 h to minimize contamination by argon.

one state point at 250 K and 34 MPa and for the 300 K isotherm over a pressure range from 10 to 32 MPa with data by Straty and Younglove,17 cf. Figure 2.

Figure 2. Comparison of speed of sound data for oxygen at 300 K measured by Straty and Younglove17 (▽) and in the present work (☆) with the equation of state (EOS) by Schmidt and Wagner.1

Speed of sound measurements of compressed oxygen in the supercritical state over a temperature range from 300 to 500 K and a pressure of up to 100 MPa were carried out with the pulse-echo technique.21 The measurement principle was based on a sample cell that has two known propagation path lengths l1 and l2, where l2 > l1.22 By emitting a modulated high frequency wave burst with a piezoelectric quartz crystal with a resonance frequency of 8 MHz, which was positioned between two reflectors in the fluid, the speed of sound c was determined by the time measurement of the wave propagation through the fluid. Applying a Fourier transformation based digital filter on the sampled acoustic wave signals increased their signal-tonoise ratio and enhanced their time and amplitude resolutions, improving the overall measurement accuracy.23 In addition, burst design led to technical advantages for determining the propagation time due to the associated conditioning of the echo. A complete description of the method, apparatus and discussion of uncertainties has been published in preceding work.24,25

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RESULTS AND DISCUSSION The measuring cell was filled at low temperatures of around 250 K, closed, and then heated up to each studied isotherm. This isochoric pressurizing has a low risk of an increase of temperature through adiabatic compression by a feed pump or by a pressure surge in the piping system. Measurements were carried out from high to low pressure by releasing fluid to the ambient through a valve. Below a pressure of 5 MPa, measurements were not feasible due to the usual limitations of the pulse-echo technique, such as acoustic impedance and attenuation. These effects predominantly play a role in low density fluids, i.e., gases up to the critical region and other highly attenuating liquids, and impede the readability of the echoes due to their distortion, temporal extension and low amplitude.25 The first measurement was performed for a data point at 250 K and 34 MPa and showed a good agreement in a range of 0.07% with the data by Straty and Younglove,17 which is within the stated uncertainty. The overall uncertainty of the temperature measurement with a Pt 100 thermometer (Rössel Messtechnik RM-type) was less than uc,ΔT = 30 mK. The

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SAFETY REQUIREMENTS FOR HANDLING OXYGEN When working with pure oxygen, especially at high temperatures and pressures, tight safety requirements have to be met because it supports combustion and corrosion. Being highly oxidizing, it reacts vigorously with combustible materials and enhances fire or explosion, liberating large amounts of energy in a short time. A chemical reaction in an oxygen environment takes place, if the activation energy (i.e., ignition temperature) of a material is exceeded. To prevent temperature peaks by adiabatic pressure surges, high fluid velocities through valves etc. of the apparatus should be avoided. Therefore, charging and discharging the measuring cell with oxygen through the piping system was done here very gently. Furthermore, the apparatus had to be free of welding beads and swarfs due to their sensitivity to pressure surges.26−28 The technical norm DIN EN 1797 introduces a method for testing the behavior of materials exposed to pressure surges, which can be caused by adiabatic compression or high gas

Table 1. Sample Table

B

chemical name

source

impurity

purification method

argon oxygen

Air Liquide Air Liquide

≤10 ppm ≤15 ppm

none none



Article

Table 2. Experimental Data for the Speed of Sound of Oxygena T (K)

p (MPa)

c (m/s)

±uc (m/s)

T (K)

c (m/s)

±uc (m/s)

299.997 299.966 299.966 299.968 299.966 299.966 299.967 299.969 299.972 299.971 299.970 299.969 299.965 299.967

74.03 69.69 64.96 60.16 55.14 50.01 45.03 39.96 34.96 29.96 25.03 20.05 14.86 9.92

645.07 624.95 602.28 578.47 552.86 525.82 498.92 471.20 443.87 417.33 392.82 370.99 352.65 340.22

0.93 0.95 0.98 1.01 1.04 1.06 1.08 1.09 1.08 1.03 0.94 0.09 0.08 0.08

399.090 399.091 399.092

7.95 6.02 4.96

393.26 389.77 388.03

0.08 0.08 0.08

349.976 349.987 350.030 349.988 349.985 349.983 349.986 350.033 349.987 349.977 349.988 349.988 349.990 349.988 349.978

78.85 68.69 64.93 59.91 55.11 49.90 45.02 40.05 35.08 29.99 24.98 19.64 14.98 10.07 8.03

641.85 600.07 584.11 562.59 541.66 518.73 497.15 475.39 454.09 433.29 414.20 396.03 382.53 370.90 367.01

0.82 0.85 0.86 0.88 0.88 0.89 0.88 0.87 0.84 0.79 0.72 0.09 0.08 0.08 0.08

449.950 449.794 449.883 449.867 449.877 449.887 449.888 449.896 449.896 449.939 449.940 449.934 449.934 449.935 449.938 449.943 449.944 449.936 449.948 449.941

88.05 87.52 85.02 80.01 75.27 70.12 65.18 60.07 55.09 49.91 45.09 40.05 35.03 30.00 24.94 20.01 15.00 9.97 8.01 6.01

662.01 660.32 652.33 636.12 620.61 603.58 587.16 570.12 553.54 536.52 520.58 504.35 488.60 473.40 458.85 445.60 433.26 422.01 418.16 414.33

0.67 0.68 0.68 0.68 0.69 0.69 0.69 0.69 0.68 0.67 0.66 0.65 0.62 0.59 0.56 0.09 0.09 0.09 0.09 0.09

399.051 399.066 399.072 399.083 399.082 399.077 399.080 399.086 399.083 399.081 399.084 399.089 399.092 399.064 399.095 399.109

83.18 79.99 74.59 70.10 64.90 60.07 54.97 50.09 44.98 39.97 34.89 29.90 25.01 19.90 15.01 9.98

648.15 636.78 617.20 600.65 581.28 563.14 543.88 525.43 506.29 487.82 469.60 452.47 436.72 421.58 408.72 397.34

0.74 0.75 0.76 0.76 0.77 0.77 0.77 0.76 0.75 0.73 0.71 0.67 0.62 0.09 0.09 0.08

498.908 498.901 498.906 498.925 498.918 498.908 498.833 498.895 498.888 499.030 499.026 499.004 498.990 499.000 498.999 499.014 499.037 499.016 498.943 499.026 499.031 499.027

100.06 95.00 90.00 84.89 79.99 74.96 69.94 65.00 60.01 54.81 49.93 44.90 40.01 34.73 29.91 24.90 20.07 14.94 10.00 7.82 5.91 4.92

699.53 684.96 670.28 655.27 640.74 625.69 610.55 595.63 580.54 564.89 550.29 535.41 521.13 506.11 492.81 479.52 467.39 455.31 444.64 440.23 436.52 434.71

0.62 0.62 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.62 0.61 0.60 0.59 0.57 0.54 0.52 0.10 0.09 0.09 0.09 0.09 0.09

p (MPa)

a Standard uncertainties u are u(T) = 0.03 K, u(p) = 0.2 MPa for p ≥ 20 MPa, and u(p) = 0.01 MPa for p ≤ 20 MPa where u(p) contributed around 95% above 20 MPa and around 40% below 20 MPa to the combined uncertainty uc.

isotherms 300 and 350 K up to a pressure of 40 MPa with pure argon (cf. Table 1) using values calculated from the EOS by Tegeler et al.37 with an uncertainty uEOS = 0.02%. Here, the temperature was measured with the same Pt 100 thermometer which was used during the present oxygen measurements, and the pressure was measured with a dead weight tester (DHBudenberg 580 EHX) with an overall absolute uncertainty uc,Δp,REF = 0.02%. According to the error propagation law, the combined speed of sound measurement uncertainty uc is composed of the

pressure was measured with two transducers (Honeywell TJE), one with a measuring range from 0 to 20 MPa and the second one with a measuring range up to 200 MPa. The first one had an uncertainty of ±0.05% and the second one of ±0.1% with respect to their full scale and therefore had a maximum absolute uncertainty of ±0.2 MPa above 20 MPa, which had the largest impact at low temperatures. This is a consequence of the pressure uncertainty, combined with the high isothermal compressibility of the fluid at such thermodynamic states. The propagation path lengths were referenced at the two C



Article

Steeper slopes of the isotherms at lower temperatures for the speed of sound as a function of pressure in the supercritical region can also be observed for other diatomic fluids like nitrogen (measurements by Costa Gomez et al.38) or hydrogen (equation of state by Leachman et al.39) at comparable states (cf. Figure 3 (top)). Due to the large contribution of the pressure uncertainty (for measurements above 20 MPa around 95% and below 20 MPa around 40%) to the overall uncertainty, uc has its maximum of almost 0.25% for the data point at 300 K and 30 MPa, cf. Figure 3 (bottom). This work covered a wide range of temperature and pressure in the supercritical state for which no experimental data were available for oxygen. The present results show that the pulseecho technique is a reliable and accurate method for the measurement of the speed of sound of supercritical oxygen.

relevant contributions due to uncertainties of temperature (in this case twice, i.e., for referencing and measuring) and pressure measurements, as well as the uncertainties of the referencing procedure uc =

2(uc, ΔT )2 + (uc, Δp)2 + (uEOS)2 + (uc, Δp ,REF)2

(1)

The uncertainty of the operation procedure was limited by the internal time reference of the function generator and was thus neglected. Likewise the uncertainty of the very low impurity of oxygen (cf. Table 1) was not considered. Numerical experimental data together with their uncertainties are listed in Table 2.

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CONCLUSION

The speed of sound of oxygen was measured in the supercritical region along five isotherms from 300 to 500 K and from somewhat above 5 MPa up to 100 MPa. The measured speed of sound data for oxygen were compared with the EOS by Schmidt and Wagner.1 The uncertainties of the EOS which is valid in the temperature range from the triple point to 300 K and a pressure of up to 80 MPa were stated as 1% for the speed of sound, except for the critical region. The present measurements confirm this uncertainty and show that for temperatures above 400 K the maximum deviation increases to about 1.6%, cf. Figure 3.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49-5251/ 60-2421. Fax: +49-5251/60-3522. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Christian Binder, Thomas Kasch, and Siegfried Lehné of the Bundesamt für Materialforschung (BAM) in Berlin for consultancy about safety issues with respect to pure oxygen.

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REFERENCES

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Figure 3. Absolute values (top) and deviations (bottom) of present experimental speed of sound data from the equation of state (EOS) for oxygen by Schmidt and Wagner1 at ●, 300 K; ○, 350 K; ▼, 400 K; △, 450 K and ■, 500 K. D



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Speed of Sound of Oxygen in Supercritical States up to 500 K and 100

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